Question

A ring of radius 0.1m is made out of a thin metallic wire of area of cross- section 10-6m2. The ring has a uniform charge of coulomb. Find the change in the radius of the ring when a charge of 10-8 coulomb is placed at the centre of the ring. Young's modulus of the metal is 2x1011 n/m2 .

Answer 1

We know that from the given radius of the ring is r=0.1 m

And charge per unit length of the ring will be considered with every small amount of element AB to the wire.

Let us consider dl=AB for the element and the charge q0 as shown in the image with an element of repulsive force.

As dl is very small,  so the θ is also small and for small values of θ, sinθ, where θ is in radians.

Now the stress=F/A. If the Δr is changing now the radius of the wire, then it will be.